Related papers: Fox-H densities and completely monotone generalize…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state…

In this paper, we apply the ratio conjecture of $L$-functions to derive the lower order terms of the $1$-level density of the low-lying zeros of a family quadratic Hecke $L$-functions in the Gaussian field. Up to the first lower order term,…

Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…

Let $d$ be a positive integer and $\mathbb H$ be an integrally closed subring of a global function field $F$. The purpose of this paper is to provide a general sieve method to compute densities of subsets of $\mathbb H^d$ defined by local…

This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…

We study random one-Lipschitz integer functions $f$ on the vertices of a finite connected graph, sampled according to the weight $W(f) = \prod_{\langle v, w \rangle \in E} \mathbf{c}^{ \mathbb{I} \{ f(v) = f(w) \} }$ where $\mathbf{c} \geq…

We explore the analytic properties of the density function $ h(x;\gamma,\alpha) $, $ x \in (0,\infty) $, $ \gamma > 0 $, $ 0 < \alpha < 1 $ which arises from the domain of attraction problem for a statistic interpolating between the…

We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based…

Starting from the Davenport-Heilbronn function equation: $f(s) = X(s) f(1-s)$, we discover the four properties of the meromorphic function $X(s)$ defined as the ratio of the Davenport-Heilbronn functions: $\frac{f(s)}{f(1-s)} = X(s)$, and…

This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…

Using $\sim 100$ X-ray selected clusters in the Dark Energy Survey Science Verification data, we constrain the luminosity function (LF) of cluster red sequence galaxies as a function of redshift. This is the first homogeneous optical/X-ray…

A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a…

We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are…

[Abridged] We present new measurements of the H-alpha luminosity function (LF) and SFR volume density for galaxies at z~0.8. Our analysis is based on 1.18$\mu$m narrowband data from the NEWFIRM H-alpha Survey, a comprehensive program…

In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. They were introduced by the author in complexity classification of minimum…

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of…

Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some…

A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic…

A family of random variables $\mathbf{X}(s)$, depending on a real parameter $s>-\frac{1}{2}$, appears in the asymptotics of the joint moments of characteristic polynomials of random unitary matrices and their derivatives, in the ergodic…